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The error is that the probability of winning is not 0.5, it’s a function of how much they have in their wallet. They probably don’t know the true distribution s
by zeroonetwothree 4y ago
The error is that the probability of winning is not 0.5, it’s a function of how much they have in their wallet. They probably don’t know the true distribution so they can’t calculate the actual expected value. But clearly your chance of winning is better if you have $1 than if you have $100000
- robocat 4y agoSo add a step: they flip a coin and swap wallets if it comes up heads. Now what is the probability of each winning? Did adding that step actually change the problem? Or reword the problem just like I did in my grandparent comment: call the amount in the larger wallet $X. If you lose then you lose $X, and if you win then you win $X. 50% chance and expected outcome $X/2 by playing.